Compact SOP Representations for Multiple-Output Functions: An Encoding Method Using Multiple-Valued Logic

This paper shows a method to represent a multipleoutput function: Encoded characteristic function for nonzero outputs (ECFN). The ECFN uses (n+ u) binary variables to represent an n-input m-output function, where u = dlog2 me. The size of the sum-of-products expressions (SOPs) depends on the encoding method of the outputs. For some class of functions, the optimal encoding produces SOPs with O(n) products, while the worst encoding produces SOPs with O(2) products. We formulate encoding problem and show a heuristic optimization method. Experimental results using standard benchmark functions show the usefulness of the method. Index term: Multiple-output function, encoding problem, multiple-valued logic, TDM, SOP, characteristic function.